This prior is a reason to reject the argument (every decision to accept or reject a conclusion can be reduced to a choice of priors), and since it is willing to abandon all beliefs which contradict its rejection it will not hold any contradictory beliefs.
You're right that I am committed to denying this, though I would also point out that it does not follow a priori that it is always possible to resolve the state of having contradictory beliefs by rejecting either side of a contradiction arbitrarily. However, in order to deny the above, I must claim that there are some beliefs a mind holds (or is committed to, where this means that these beliefs are deductively provable from what the mind does believe) just in virtue of being a mind. I'll bite that bullet, and claim that there exists a UCMA of this kind. I also think the Law of Non-Contradiction is a UCA, and in fact it's trivially so on my definition, but I think that'll hold up: there are no Bayesian reasons to think that ascribing it a probability of 1 is a problem, and I do think I can defend the claim that evidence against it is a priori impossible (EY's example reasons for doubt in the two articles you cite wouldn't apply in this case).
You have to define which minds have to be persuaded somewhere between a tape recorder shouting "2 + 2 = 5!" for eternity and including only your brain's algorithm. And where you draw that line determines exactly which arguments, if any, are UCMAs.
This isn't a problem on my definition of a UCA. My understanding of a UCA (which I think represents an honest to god position, namely Kant's) is consistant with any given mind believing the UCA to be false, perhaps because of reasons like the tape-recorder. Only, such a mind couldn't have consistant beliefs.
And if you don't have to persuade any minds, then I hesitate to permit you to call your argument "universally compelling" in any context where I can act to prevent it.
Remember that my definition of a UCMA isn't 'any mind under any circumstances could always be persuaded'. To attack this view of UCMAs is, I think, to attack a strawman. If we must take UCMAs to be arguments which are universally and actually persuasive for any mind in any circumstance in order to see EY's point (here or elsewhere) as valid, then this is a serious critique of EY.
Be very, very cautious assigning probability 1 to the proposition that you even understand what the Law of Contradiction means. How confident are you that logic works like you think it works; that you're not just spouting gibberish even though it seems from the inside to make sense. If you'd just had a major concussion, with severe but temporary brain damage, would you notice? Are you sure? After such damage you might claim that "if bananas then clocks" was true with certainty 1, and feel from the inside like you we're making sense. Don't just di... (read more)
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.